def test_hybrid_prognostic_solve():
Lx, Ly = 20e3, 20e3
h0, dh = 500.0, 100.0
T = 254.15
u_in = 100.0
model = icepack.models.HybridModel()
opts = {'dirichlet_ids': [1], 'side_wall_ids': [3, 4], 'tol': 1e-12}
Nx, Ny = 32, 32
mesh2d = firedrake.RectangleMesh(Nx, Ny, Lx, Ly)
mesh = firedrake.ExtrudedMesh(mesh2d, layers=1)
V = firedrake.VectorFunctionSpace(mesh,
dim=2,
family='CG',
degree=2,
vfamily='GL',
vdegree=1)
Q = firedrake.FunctionSpace(mesh,
family='CG',
degree=2,
vfamily='DG',
vdegree=0)
x, y, ζ = firedrake.SpatialCoordinate(mesh)
height_above_flotation = 10.0
d = -ρ_I / ρ_W * (h0 - dh) + height_above_flotation
ρ = ρ_I - ρ_W * d**2 / (h0 - dh)**2
Z = icepack.rate_factor(T) * (ρ * g * h0 / 4)**n
q = 1 - (1 - (dh / h0) * (x / Lx))**(n + 1)
ux = u_in + Z * q * Lx * (h0 / dh) / (n + 1)
u0 = interpolate(firedrake.as_vector((ux, 0)), V)
thickness = h0 - dh * x / Lx
β = 1 / 2
α = β * ρ / ρ_I * dh / Lx
h = interpolate(h0 - dh * x / Lx, Q)
h_inflow = h.copy(deepcopy=True)
ds = (1 + β) * ρ / ρ_I * dh
s = interpolate(d + h0 - dh + ds * (1 - x / Lx), Q)
b = interpolate(s - h, Q)
C = interpolate(α * (ρ_I * g * thickness) * ux**(-1 / m), Q)
A = firedrake.Constant(icepack.rate_factor(T))
final_time, dt = 1.0, 1.0 / 12
num_timesteps = int(final_time / dt)
u = model.diagnostic_solve(u0=u0, h=h, s=s, C=C, A=A, **opts)
a0 = firedrake.Constant(0)
a = interpolate((model.prognostic_solve(dt, h0=h, a=a0, u=u) - h) / dt, Q)
for k in range(num_timesteps):
h = model.prognostic_solve(dt, h0=h, a=a, u=u, h_inflow=h_inflow)
s = icepack.compute_surface(h=h, b=b)
u = model.diagnostic_solve(u0=u, h=h, s=s, C=C, A=A, **opts)
assert icepack.norm(h, norm_type='Linfty') < np.inf
def test_computing_surface():
N = 16
mesh = firedrake.RectangleMesh(N, N, Lx, Ly)
degree = 2
Q = firedrake.FunctionSpace(mesh, "CG", degree)
x, y = firedrake.SpatialCoordinate(mesh)
h = interpolate(h0 - dh * x / Lx, Q)
b0 = ρ_I / ρ_W * (dh / 2 - h0)
b = interpolate(firedrake.Constant(b0), Q)
s = icepack.compute_surface(thickness=h, bed=b)
x0, y0 = Lx / 2, Ly / 2
assert abs(s((x0, y0)) - (1 - ρ_I / ρ_W) * h((x0, y0))) < 1e-8
opts = {
'dirichlet_ids': [1],
'side_wall_ids': [3, 4],
'diagnostic_solver_type': 'petsc',
'diagnostic_solver_parameters': {
'snes_type': 'newtontr',
'ksp_type': 'preonly',
'pc_type': 'lu',
'pc_factor_mat_solver_type': 'mumps'
}
}
solver = icepack.solvers.FlowSolver(model, **opts)
# Create the initial data
h = h0.copy(deepcopy=True)
s = icepack.compute_surface(thickness=h, bed=z_b)
a = firedrake.interpolate(firedrake.Constant(0.3), Q)
u = solver.diagnostic_solve(
velocity=u0,
thickness=h,
surface=s,
fluidity=A,
friction=C
)
# Run the simulation
δt = args.timestep
num_steps = int(args.time / δt)
output_name = os.path.splitext(args.output)[0]
def test_hybrid_prognostic_solve(solver_type):
Lx, Ly = 20e3, 20e3
h0, dh = 500.0, 100.0
T = 254.15
u_in = 100.0
model = icepack.models.HybridModel()
opts = {
'dirichlet_ids': [1],
'side_wall_ids': [3, 4],
'prognostic_solver_type': solver_type
}
Nx, Ny = 32, 32
mesh2d = firedrake.RectangleMesh(Nx, Ny, Lx, Ly)
mesh = firedrake.ExtrudedMesh(mesh2d, layers=1)
V = firedrake.VectorFunctionSpace(
mesh, 'CG', 2, vfamily='GL', vdegree=1, dim=2
)
Q = firedrake.FunctionSpace(mesh, 'CG', 2, vfamily='DG', vdegree=0)
x, y, ζ = firedrake.SpatialCoordinate(mesh)
height_above_flotation = 10.0
d = -ρ_I / ρ_W * (h0 - dh) + height_above_flotation
ρ = ρ_I - ρ_W * d**2 / (h0 - dh)**2
Z = icepack.rate_factor(T) * (ρ * g * h0 / 4)**n
q = 1 - (1 - (dh/h0) * (x/Lx))**(n + 1)
ux = u_in + Z * q * Lx * (h0/dh) / (n + 1)
u0 = interpolate(firedrake.as_vector((ux, 0)), V)
thickness = h0 - dh * x / Lx
β = 1/2
α = β * ρ / ρ_I * dh / Lx
h = interpolate(h0 - dh * x / Lx, Q)
h_inflow = h.copy(deepcopy=True)
ds = (1 + β) * ρ / ρ_I * dh
s = interpolate(d + h0 - dh + ds * (1 - x / Lx), Q)
b = interpolate(s - h, Q)
C = interpolate(α * (ρ_I * g * thickness) * ux**(-1/m), Q)
A = firedrake.Constant(icepack.rate_factor(T))
final_time, dt = 1.0, 1.0/12
num_timesteps = int(final_time / dt)
solver = icepack.solvers.FlowSolver(model, **opts)
u = solver.diagnostic_solve(
velocity=u0, thickness=h, surface=s, fluidity=A, friction=C
)
a = firedrake.Function(Q)
h_n = solver.prognostic_solve(
dt, thickness=h, velocity=u, accumulation=a, thickness_inflow=h_inflow
)
a.interpolate((h_n - h) / dt)
for k in range(num_timesteps):
h = solver.prognostic_solve(
dt,
thickness=h,
velocity=u,
accumulation=a,
thickness_inflow=h_inflow
)
s = icepack.compute_surface(thickness=h, bed=b)
u = solver.diagnostic_solve(
velocity=u,
thickness=h,
surface=s,
fluidity=A,
friction=C
)
assert icepack.norm(h, norm_type='Linfty') < np.inf
def test_ice_stream_prognostic_solve():
Lx, Ly = 20e3, 20e3
h0, dh = 500.0, 100.0
T = 254.15
u0 = 100.0
model = icepack.models.IceStream()
opts = {"dirichlet_ids": [1], "side_wall_ids": [3, 4]}
N = 32
mesh = firedrake.RectangleMesh(N, N, Lx, Ly)
V = firedrake.VectorFunctionSpace(mesh, "CG", 2)
Q = firedrake.FunctionSpace(mesh, "CG", 2)
solver = icepack.solvers.FlowSolver(model, **opts)
x, y = firedrake.SpatialCoordinate(mesh)
height_above_flotation = 10.0
d = -ρ_I / ρ_W * (h0 - dh) + height_above_flotation
ρ = ρ_I - ρ_W * d**2 / (h0 - dh)**2
Z = icepack.rate_factor(T) * (ρ * g * h0 / 4)**n
q = 1 - (1 - (dh / h0) * (x / Lx))**(n + 1)
ux = u0 + Z * q * Lx * (h0 / dh) / (n + 1)
u0 = interpolate(firedrake.as_vector((ux, 0)), V)
thickness = h0 - dh * x / Lx
β = 1 / 2
α = β * ρ / ρ_I * dh / Lx
h = interpolate(h0 - dh * x / Lx, Q)
h_inflow = h.copy(deepcopy=True)
ds = (1 + β) * ρ / ρ_I * dh
s = interpolate(d + h0 - dh + ds * (1 - x / Lx), Q)
b = interpolate(s - h, Q)
C = interpolate(α * (ρ_I * g * thickness) * ux**(-1 / m), Q)
A = Constant(icepack.rate_factor(T))
final_time, dt = 1.0, 1.0 / 12
num_timesteps = int(final_time / dt)
u = solver.diagnostic_solve(
velocity=u0,
thickness=h,
surface=s,
fluidity=A,
friction=C,
strain_rate_min=Constant(0.0),
)
a = firedrake.Function(Q)
h_n = solver.prognostic_solve(dt,
thickness=h,
velocity=u,
accumulation=a,
thickness_inflow=h_inflow)
a.interpolate((h_n - h) / dt)
for k in range(num_timesteps):
h = solver.prognostic_solve(dt,
thickness=h,
velocity=u,
accumulation=a,
thickness_inflow=h_inflow)
s = icepack.compute_surface(thickness=h, bed=b)
u = solver.diagnostic_solve(
velocity=u,
thickness=h,
surface=s,
fluidity=A,
friction=C,
strain_rate_min=Constant(0.0),
)
assert icepack.norm(h, norm_type="Linfty") < np.inf